Question: Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}4x-6y &= -7 \\ 4x-3y &= 2\end{align*}$
Answer: Begin by moving the $y$ -term in the second equation to the right side of the equation. $4x = 3y+2$ Divide both sides by $4$ to isolate $x$ $x = {\dfrac{3}{4}y + \dfrac{1}{2}}$ Substitute this expression for $x$ in the first equation. $4({\dfrac{3}{4}y + \dfrac{1}{2}}) - 6y = -7$ $3y + 2 - 6y = -7$ Simplify by combining terms, then solve for $y$ $-3y + 2 = -7$ $-3y = -9$ $y = 3$ Substitute $3$ for $y$ in the top equation. $4x-6( 3) = -7$ $4x-18 = -7$ $4x = 11$ $x = \dfrac{11}{4}$ The solution is $\enspace x = \dfrac{11}{4}, \enspace y = 3$.